This note is an example of the knapsack crypto-system at work.So before you got through this note I recommend reading the main one . Click here
Suppose that a typical user of this crypto-system selects as the secret key the super-increasing sequence and the modulus and the multiplier .Each member of the super-increasing sequence is multiplied by 44 and reduced modulo 85 to yield .This is the encryption key the user submit to the public directory.
Suppose someone wants to send a plaintext message to the user such as "HELP US". First we convert it into a string of 1's and 0's The string is then broken up into blocks of digits,in the current case,blocks of length 5.Using the listed public keys to encrypt,the sender transforms the successive blocks into
The transmitted ciphertext consists of the following series of positive integers .
To read the message the legitimate receiver first solves the congruence ,yielding .Then each ciphertext number is multiplied by 29 and reduced modulo 85 to produce a super-increassing knapsack problem.
For example, is converted to as and the corresponding knapsack problem is .
The procedure for solving super-increasing knapsack problems quickly yields the solution ,,in this way ,the first block of the binary equivalent of the plaintext is obtained.